Question 426848
Divide both sides of the equation by 2, to get {{{x^2-2x-3/2 = 0}}}. For complex or radical roots, the conjugate must also be a root.  The conjugate of the root that you got is {{{1 + 2sqrt(5)}}}.

The sum of the roots must be equal to -(-2), or 2.  This is true, as {{{(1 -  2sqrt(5)) + (1 + 2sqrt(5)) = 2}}}.
The product of the roots must be -3/2.  This is not true, as {{{(1 -  2sqrt(5))*(1 + 2sqrt(5)) = 1 - 4*5 = -19}}}.
Hence the root that you got is incorrect.